Problem: Stephanie is 5 times as old as Kevin. Four years ago, Stephanie was 7 times as old as Kevin. How old is Kevin now?
Answer: We can use the given information to write down two equations that describe the ages of Stephanie and Kevin. Let Stephanie's current age be $s$ and Kevin's current age be $k$ The information in the first sentence can be expressed in the following equation: $s = 5k$ Four years ago, Stephanie was $s - 4$ years old, and Kevin was $k - 4$ years old. The information in the second sentence can be expressed in the following equation: $s - 4 = 7(k - 4)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to use our first equation for $s$ and substitute it into our second equation. Our first equation is: $s = 5k$ . Substituting this into our second equation, we get: $5k$ $-$ $4 = 7(k - 4)$ which combines the information about $k$ from both of our original equations. Simplifying the right side of this equation, we get: $5 k - 4 = 7 k - 28$ Solving for $k$ , we get: $2 k = 24.$ $k = 12$.